Intuitively, a larger classification margin allows a classifier to associate a larger region centered on a point \(x_i\)  in the input space to the same class.
This makes the classifier less sensitive to input perturbations, and a perturbation of \(x_i\)  is still likely to fall within this region, keeping the classifier prediction.
In this sense, the classifier becomes more robust. In the typical case, the networks are trained by a loss (cross-entropy) that promotes separation of different classes in the network output. This, in turn, maximizes a certain notion of score of each training sample [1]}.
